e = quote(e) -- clear e, was exponential, now elementary charge -- E is total energy E = hbar^2 / (2 mu a0^2) - e^2 / (4 pi epsilon0 a0) dE = d(E,a0) -- Bohr radius minimizes total energy a0 = 4 pi epsilon0 hbar^2 / (e^2 mu) "Bohr radius" a0 "Verify that total energy is minimized for Bohr radius (1=ok)" dE == 0 -- base units ampere = "ampere" kilogram = "kilogram" meter = "meter" second = "second" -- derived units coulomb = ampere second farad = ampere^2 kilogram^(-1) meter^(-2) second^4 joule = kilogram meter^2 second^(-2) volt = ampere^(-1) kilogram meter^2 second^(-3) "Numerical value for Bohr radius" pi = float(pi) hbar = 1.054572 10^(-34) joule second -- Planck's constant epsilon0 = 8.854188 10^(-12) farad / meter -- electric constant e = 1.602176 10^(-19) coulomb -- elementary charge me = 9.109382 10^(-31) kilogram -- mass of electron mp = 1.672622 10^(-27) kilogram -- mass of proton mu = me mp / (me + mp) a0 "Numerical value for Rydberg unit of energy" -E 1/(1.602177 10^(-19)) "electron-volt" / joule